Fundamentals of Inorganic Non-metallic Materials Science

Author: Fan Xianping, Hong Zhanglian, Weng Wenjian (editors)
Publisher:
Publish Date: 2004-08-01
Features: 2. Diffusion of Reactants Through the Product Layer
When reactants form a product layer, one or more reactants must diffuse through the product layer for the reaction to continue. The diffusion laws in solid-state reactions are the same as general diffusion laws. Therefore, to facilitate a deeper understanding of the kinetic processes in solid-state reactions, a brief description of the diffusion phenomena and laws in solid-state reactions will be provided in the following Section 2.
Section 2: Solid-State Defects and Diffusion
The basic theories introduced in this section, such as chemical bonding, crystal chemistry principles, and basic crystal structure types, are based on ideal crystals. In actual materials, there is often an irregular arrangement of point units (atoms or molecules), i.e., certain crystal structure defects exist.
As mentioned in this section, some basic defect types, such as point defects, line defects, and planar defects, have been introduced, with a focus on the discussion of solid solutions—a fundamental, common, and very important type of point defect. The various defects present in actual crystals not only affect the structure and performance of materials but also play a very significant, even decisive, role in material preparation processes.
The diffusion of mass transfer mentioned earlier is a very important process in solid-state reactions, and the various lattice defects in the crystal structure are one of the most important factors affecting the diffusion process. Considering the significant role of various defects and their physicochemical behaviors in solid-state reactions and sintering, this section further elaborates on the defects and diffusion phenomena involved in solid-state reactions and sintering based on the defect theory introduced in this section.
### 1. Common Defect Types
As mentioned earlier, solid-state crystal defects can be divided into three major categories based on geometric dimension and combined morphology: point defects, line defects, and planar defects.
#### 1.1 Point Defects
Point defects generally occur at or near the positions of lattice points in the crystal structure, with almost no three-dimensional scale, and are also known as zero-dimensional defects. Common types include vacancies, interstitial atoms, and substitutional atoms (solid solutions); in addition, vacancy pairs formed by them are also considered point defects.
#### 1.2 Line Defects
Line defects are distributed along one dimension and can sometimes be seen as the connection and extension of point defects in one dimension, also known as one-dimensional defects. The most common type is dislocations.
#### 1.3 Planar Defects
Planar defects are defects distributed in two dimensions and are also known as two-dimensional defects. Common types include crystal surfaces, grain boundaries, phase boundaries, and stacking faults.
### 2. Point Defects and Their Research Methods
#### 2.1 The Production of Point Defects
From a thermodynamic perspective, point defects can be divided into two types: thermodynamically equilibrium point defects and non-equilibrium point defects. Correspondingly, the production of point defects generally follows two pathways: thermodynamic equilibrium pathways and non-equilibrium pathways (under the action of certain external fields).
##### (1) Thermodynamic Equilibrium Pathways
Based on their causes of formation, the formation of thermodynamically equilibrium point defects can be divided into three basic pathways: thermal vibration (physical pathway), non-stoichiometric defects, and impurity doping (chemical pathway). Among these, thermal vibration is the most fundamental defect production pathway. In ideal stoichiometric crystals or non-ideal stoichiometric crystals, thermal vibration can produce equilibrium point defects such as "vacancies" and "self-interstitial atoms." Generally, under conditions that are not absolute zero, all atoms in a crystal vibrate around their equilibrium positions. The higher the temperature, the greater the average energy of atomic thermal vibrations. Moreover, the thermal vibration energy of each atom at the same time is not the same, and there is a distribution around the average energy at this temperature, always undergoing constant fluctuations, known as energy fluctuations. Energy fluctuations cause some atoms to have higher energy. When the fluctuation energy is high enough to overcome the binding force of surrounding atoms, they may migrate to other places, leading to the formation of vacant sites at their original equilibrium positions, known as "vacancies." Based on the destination of the displaced atoms, vacancies can be divided into two major types: Schottky vacancies and Frankel vacancies. Vacancies that remain at the outer surface or inner interfaces (such as grain boundaries) are called Schottky vacancies. If the displaced atoms migrate to the interstitial sites of the crystal lattice, they form Frankel vacancies, along with an equal number of interstitial atoms. In addition to "vacancies," there are also equilibrium point defects known as "self-interstitial atoms." Under the mechanism of thermal vibration, the inherent atoms of the crystal migrate from the outer surface or inner interfaces to interstitial positions within the crystal, forming "self-interstitial atoms." Generally, there are two sources of interstitial atoms: one is the aforementioned inherent atoms (self-interstitial atoms), and the other is foreign interstitial atoms, which will be discussed below. Through impurity doping (chemical pathway), a variety of equilibrium point defects with controllable concentrations can be introduced. Generally, the changes in the types and concentrations of defects introduced through the doping pathway (such as vacancies, interstitial atoms, etc.) can be studied and expressed in the form of defect reaction equations by analyzing the radius, valence, and crystal structure of the dopants. The equilibrium point defects analyzed above can exist in ionic crystals, covalent crystals, metallic crystals, and other crystal structures. However, the types and concentration patterns of defects vary significantly depending on the material due to differences in bonding properties and requirements for electrical neutrality among different crystal structures. For example, metallic crystals do not have requirements for electrical neutrality, while ionic crystals not only require overall electrical neutrality but also local electrical neutrality. Therefore, Schottky point defects in ionic crystals require an equal number of positive ion vacancies and negative ion vacancies. Additionally, due to the much larger radius of negative ions compared to positive ions in ionic crystals, Frankel defects in ionic crystals can only consist of an equal number of positive ion vacancies and positive ion interstitial atoms.
##### (2) Thermodynamic Non-Equilibrium Pathways
At room temperature, the concentration of thermodynamically equilibrium point defects produced by thermal vibration in a crystal is very low. Through certain special processes, under thermodynamic non-equilibrium conditions, the crystal can have a point defect concentration higher than the equilibrium concentration, known as thermodynamically non-equilibrium point defects (also called supersaturated point defects). Below, we will introduce several methods for obtaining thermodynamically non-equilibrium point defects.
###### (i) High-Temperature Quenching Method
Generally, as the temperature increases, the concentration of thermodynamically equilibrium point defects also increases. Therefore, heating the crystal to a high temperature forms a large number of vacancies in the crystal. Then, using a rapid cooling method (quenching), the crystal is quickly cooled from high to low temperature, so that the vacancies do not disappear during the cooling process, allowing supersaturated vacancies to form at low temperatures. This quenching method is also a common and effective means of studying crystal defects in high-temperature states under room temperature conditions.
###### (ii) High-Energy Irradiation Method
The high-energy particles used in irradiation methods mainly include fast neutrons, heavy particles, and electrons. For example, in an atomic reactor, the high-speed neutrons produced by fission have an average energy of 2 MeV. When highly energetic radiation particles irradiate a crystal, their high energy knocks atoms out of the lattice sites, and these displaced atoms continue to collide with other atoms at high speeds, causing more atoms to be displaced while forming an equal number of vacancies and interstitial atoms. High-energy particle irradiation is also a very effective means of modifying materials.
###### (iii) Plastic Deformation Method
Plastic deformation uses a certain external force to apply an external effect to the material, causing the crystal material to undergo plastic deformation. This plastic deformation is often accompanied by the interaction of dislocations, and some of the external force energy is converted into defect formation energy, thus producing supersaturated point defects. Generally, the plastic deformation method is often used for processing metallic materials, and by introducing supersaturated defects, the strength of metallic materials can be improved. Ceramic materials are different from metallic materials, as they generally do not have the ability to deform plastically at room temperature or low temperatures. However, some ceramic materials have certain plastic deformation capabilities at high temperatures, and high-temperature plastic deformation of ceramics is also known as "high-temperature forging."
In summary, these supersaturated point defects are point defects under thermodynamic non-equilibrium conditions and are thermodynamically unstable. They can be eliminated through reheating, where they disappear via thermal vibration during the heating process and eventually tend to the equilibrium point defect concentration under thermodynamic conditions.
#### 2.2 The Movement of Point Defects
Vacancies and interstitial atoms disrupt the balance of interatomic forces in ideal crystals, causing elastic distortion of the lattice and the formation of a stress field, which increases the internal energy of the crystal. Therefore, defects themselves are highly active. Thermal vibration causes them to move continuously, following no fixed direction, and undergo self-diffusion. Additionally, under a certain external field (corresponding to a chemical potential), point defects can move in a specific direction, forming a material flow with a certain pattern, i.e., regular diffusion migration. Therefore, the movement of point defects can generally be divided into two types: random thermal motion and regular diffusion migration.
##### (1) Random Thermal Motion (Self-Diffusion)
Point defects are constantly moving, and below, we will take vacancies as an example to illustrate the movement of point defects. Under thermal vibration conditions, vacancies achieve their random thermal motion by continuously exchanging positions with surrounding atoms. Among these, the movement of vacancies requires overcoming a certain potential barrier (equivalent to the energy of lattice distortion caused by the point defect), and the additional energy required for this is called the migration energy. During the movement process, if a vacancy encounters an interstitial atom, the vacancy disappears, a phenomenon known as recombination. When a vacancy moves to dislocations, grain boundaries, or external surfaces, it will also disappear. Thus, under the control of energy fluctuations, point defects are constantly produced, move, and disappear. The movement of point defects is essentially the result of atomic migration, and their migration ability can be expressed through the self-diffusion coefficient. This atomic migration ability corresponds to the foundation of diffusion phenomena in solids.
##### (2) Regular Movement of Point Defects Under External Field (Diffusion Mass Transfer)
Under a certain chemical potential (such as concentration gradient, stress gradient, electric field gradient, etc.), the random diffusion caused by thermal motion becomes a material flow with a certain flow rate and direction, such as this regular movement, which is also the basis of diffusion mass transfer.
#### 2.3 Research Methods for Point Defects
Generally, point defects affect the physical and chemical properties of materials to some extent. Changes in the types and concentrations of different point defects can lead to changes in various physical and chemical properties of materials, such as material density, coefficient of thermal expansion, transport properties (such as electrical resistance of metallic materials, ion mobility in inorganic materials, etc.). Additionally, point defects can also affect other properties of materials, such as the rate of phase transformation related to diffusion, chemical heat treatment properties, mechanical strength, and plastic deformation ability at high temperatures. Therefore, when studying point defects in different materials under different conditions, the following research approach and steps can be adopted:
###### (i) Analyze the bonding properties, crystal structure types of the crystal structure units of the material, and list the possible types of point defect reactions based on the specific material.
###### (ii) Measure the variation patterns of the physical and chemical properties of the material (material density, coefficient of thermal expansion, transport properties).
###### (iii) Based on the correlation between point defects and material properties, analyze and determine the types of point defects that occur in the material, and based on the variation data of the material's physical and chemical properties (material density, coefficient of thermal expansion, transport properties), determine the concentration of the point defects that occur and their correlation with factors such as material structure and preparation conditions.